Scatterplots

Plotting two number variables

• When both variables are quantitative, show them in a scatterplot 散点图.
• Each individual is one point: explanatory value across ($x$), response value up ($y$).
• The cloud of points reveals whether — and how — the two variables move together.
• The scatterplot is the single most important graph in this unit.

Direction, form, strength

• Direction: positive (up together) or negative (one up, other down)?
• Form: roughly linear 线性 (a straight-line trend) or curved?
• Strength: how tightly do the points hug the pattern — tight, or a loose cloud?
• Describe all three, every time, in the context of the variables.

A line of best fit runs through the middle of the scattered points

Outliers and departures

• Look for outliers — points far from the overall pattern.
• Note clusters, gaps, or a bend where the form changes.
• An outlier in a scatterplot can be unusual in $x$, in $y$, or in the combination.
• Flag these departures; they often carry the most interesting information.

Describe in context

• Put it together: "As $x$ increases, $y$ tends to increase — a moderately strong, positive, linear association."
• Always name the real variables and their units, not just "$x$ and $y$."
• Mention any outlier or unusual feature explicitly.
• A complete description = direction + form + strength + unusual features, in context.

Write from a point off the pattern

• Most points on a scatterplot follow a straight upward pattern.
• One point sits far above that pattern.